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LittleWolf
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Does anyone know how to determine the probability that the sixth side of a fair die will appear on the Nth consecutive throw.
BicycleTree said:The number of onto functions from a set of size m to a set of size n is equal to the sum for i = 0 to n of ((-1)^i * C(n, i) * (n - i)^m).
So to find the answer to LittleWolf's question, you substitute N for m and 6 for n in that expression.
BicycleTree said:Looks right to me.
I think the reason it might be familiar to you is that (so says my book) the summation is a Stirling number of the second kind, S(m, n), multiplied by n!.
The probability of rolling a specific number on a six-sided die is 1/6 or approximately 16.67%. This is because there are six possible outcomes (each face of the die) and only one of them will result in the desired number.
There are 6 possible outcomes for each roll of a six-sided die. Therefore, there are 6^6 (or 46,656) different combinations that can be rolled on a six-sided die.
The expected value of rolling a six-sided die is 3.5. This is calculated by taking the sum of all possible outcomes (1+2+3+4+5+6) and dividing it by the number of outcomes (6).
No, the outcomes on each face of a die cannot be predicted. The outcome of each roll is completely random and is not affected by previous rolls or external factors.
The shape of a die, specifically the number of faces it has, is directly related to the probability of rolling a specific number. The more faces a die has, the lower the probability of rolling a specific number. For example, a ten-sided die has a lower probability of rolling a 6 compared to a six-sided die.